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The completeness of the Bethe ansatz for the periodic ASEP

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arxiv 1511.03762 v2 pith:H5AAZ2MR submitted 2015-11-12 math-ph cond-mat.stat-mechmath.AGmath.MPnlin.SI

classification math-phcond-mat.stat-mechmath.AGmath.MPnlin.SI
keywords ansatzbetheasepperiodicproofalgebraicanalyzedasymmetric
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The asymmetric simple exclusion process (ASEP) for N particles on a ring with L sites may be analyzed using the Bethe ansatz. In this paper, we provide a rigorous proof that the Bethe ansatz is complete for the periodic ASEP. More precisely, we show that for all but finitely many values of the hopping rate, the solutions of the Bethe ansatz equations do indeed yield all L choose N eigenstates. The proof follows ideas of Langlands and Saint-Aubin, which draw upon a range of techniques from algebraic geometry, topology and enumerative combinatorics.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Coordinate-energy transformation and the one-point function for the Heisenberg-Ising XXZ spin-1/2 chain on the ring

    math-ph 2025-06 conditional novelty 7.0 of 10

    An explicit inverse Bethe transformation on the periodic XXZ chain is conjectured, proven at Δ=0 and checked numerically, and used to derive a conditional exact formula for the one-point function.

  2. Riemann surfaces for KPZ with periodic boundaries

    cond-mat.stat-mech 2019-08 conditional novelty 6.0 of 10

    Known exact finite-volume KPZ fluctuation probabilities are expressed as traces on Riemann surfaces for half-integer polylogarithms, and prior formulas by Prolhac and by Baik and Liu are proved equivalent.

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